Knowledge about the distribution of CO emission in the Milky Way is essential to understanding the impact of the Galactic environment on the formation and evolution of structures in the interstellar medium. However, our current insight as to the fraction of CO in the spiral arm and interarm regions is still limited by large uncertainties in assumed rotation curve models or distance determination techniques. In this work we use the Bayesian approach from Reid et al. (2016, ApJ, 823, 77; 2019, ApJ, 885, 131), which is based on our most precise knowledge at present about the structure and kinematics of the Milky Way, to obtain the current best assessment of the Galactic distribution of 13CO from the Galactic Ring Survey. We performed two different distance estimates that either included (Run A) or excluded (Run B) a model for Galactic features, such as spiral arms or spurs. We also included a prior for the solution of the kinematic distance ambiguity that was determined from a compilation of literature distances and an assumed size-linewidth relationship. Even though the two distance runs show strong differences due to the prior for Galactic features for Run A and larger uncertainties due to kinematic distances in Run B, the majority of their distance results are consistent with each other within the uncertainties. We find that the fraction of 13CO emission associated with spiral arm features ranges from 76 to 84% between the two distance runs. The vertical distribution of the gas is concentrated around the Galactic midplane, showing full-width at half-maximum values of ~75 pc. We do not find any significant difference between gas emission properties associated with spiral arm and interarm features. In particular, the distribution of velocity dispersion values of gas emission in spurs and spiral arms is very similar. We detect a trend of higher velocity dispersion values with increasing heliocentric distance, which we, however, attribute to beam averaging effects caused by differences in spatial resolution. We argue that the true distribution of the gas emission is likely more similar to a combination of the two distance results discussed, and we highlight the importance of using complementary distance estimations to safeguard against the pitfalls of any single approach. We conclude that the methodology presented in this work is a promising way to determine distances to gas emission features in Galactic plane surveys.